I was under the impression that, as when cooked with water, flour cooked with fat will also maintain its gelatinization until it has absorbed as much as it can hold. At that point (whether it's in time, temperature, or a combination of the two, I do not know), no more thickening. You're saying it's more of a gradual slide?
Actually, I just now looked it up in Understanding Baking and while I can see that I was wrong -- flour does NOT react with fat as it does with water, and even when it has absorbed all the water it can, it continues to thicken liquid with its burst starch shells -- I still don't have an explanation for the eventual loss of thickening power. Must be because cooking starch in fat affects the cells in such a way as to prevent absorption of liquid when one is added to the other.
But my question remains: at what point does cooking flour in fat prevent its gelatinization? And it is the time, temperature, or the amount of stirring the flour-fat mixture that does it? (Stirring deflates the starch shells.)